(a) The mean and standard deviation of the wages of 1,000 factory workers are $25,600 and $2,200, respectively. If wages have a bell-shaped distribution, how many workers are expected to receive wages between $23,400 and $27,000 and between $21,200 and $30,000? Justify your answer.

(b) A manufacturing plant requires one of its suppliers to provide aluminium sheets with a special coating between 1.5 and 4.5 mm in depth. A shipment of 800 coated aluminium sheets was delivered to the plant. The plant supervisor was told that the mean depth of the coating was 3.0 mm with a standard deviation of 0.5. If there are more than 100 aluminium sheets with a coating thickness outside the range of 1.5 to 4.5 mm, should the supervisor accept the shipment? Justify your answer.

(c) In a class of 250 students, the average mark is 60, and the standard deviation is 12. Comment on the relative position of a student who scored 85. If the top 2.5% of students are awarded a High Distinction grade, should the student with a mark of 85 be awarded a High Distinction?